Monday, August 04, 2003

Simulation and Its Discontents, Part IV

I bet you thought I had forgotten about my series of posts on simulation; in fact, chances are you weren't reading my blog back then (except you, hi Dad!). I had one more point to make, but needed to figure out how to explain it.

A brief refresher for those who haven't followed the link yet: I'm a big fan of the uses of simulations, but people often overlook the problems with them. I talked about a couple of the issues, particularly the lack of certificates and the ease of being fooled by superficial structural similarity. I should have pointed out then the more obvious drawbacks: the fact that designers can easily influence the outcomes of the simulations by subtlely (and possibly invisibly) inserting their own biases. For some reason, Will Wright's preference for mass transit in SimCity is the canonical example here, despite the fact (or because?) that he's quite open about it.

Today's problem is pretty abstract, and comes via Caltech professor John Doyle. Here goes. Real life systems will change when the environment changes; some changes will create changes of larger magnitude than others, depending on the system. For example, the temperature of a house that has a functioning thermostat is fairly resistant to changes in outside temperature. If the temperature rises, the thermostat kicks in and turns on the air conditioning. Too low, and the heat comes on. However, the temperature is extremely responsive to a loss of electricity: the thermostat stops running and the temperature quickly moves into equilibrium with the outside. In short, some systems show a great deal of fragility in the face of some external perturbations, and stability in the face of others.

What Doyle's shown is that, in a model of that system, the complexity required to accurately model the system is correlated with the system's fragility. That is, for perturbations for which the system is stable, the model can be simple. For perturbations for which the model is extremely fragile, the model must be extremely complex. This is unfortunate, since it's generally in the fragile regimes that we're the most interested.